To my mind the concepts of the finite and the infinite are equally mysterious. But recently I was surprised to encounter the view that infinity may be something different from what I have instinctively thought it to be.
So in view of Plato's pythagorean background, is it true that he viewed infinity as something incomplete and imperfect, therefore unsuitable for being an attribute of God, the Demiurge?
Moreover, that it was Christianity that deeply altered the mentality towards infinity, making it an essential attribute of God? And how does it all relate to Aristotle's God as "actual" infinity, and to the fact that the infinite is always present in finite things in the form of infinite divisibility?
I hope the question is not too broad for a concise answer.
Maybe it all amounts to whether "actual infinity" is something real and not just wordplay.
Basically I'm asking for guidance for efficiently studying the history of the subject.

EDIT: So the title of the question asks whether "the infinite" is a mental construct that, although present in our minds, should not be linked to external objects with the same force & intensity that we use when we link them to "the finite", or even not at all, despite the fact that the open space surrounding us formidably suggests the idea of "infinite expansion".

  • 1
    "The infinite" isn't a thing. Neither is "the finite". This question seems to be making a puzzle out of treating an adjective like a noun, something like talking about the puzzling characteristics of "the red" or "the wet". Apr 29, 2022 at 21:21
  • @DavidGudeman -- Of course "the infinite" and "the finite" are not tangible things. They are mental constructs that can at least be related to tangible things. The question is what is the correct way to do so. Another question is whether they as well refer to non-tangible things external to the mind, if such things do exist.
    – exp8j
    Apr 30, 2022 at 7:15
  • Therefore, to ask whether "the infinite is an unsubstantial epiphenomenon of the finite" is to ask whether "the infinite" is a mental construct that, altough present in our minds, should not be linked to external objects with the same force & intensity that we use when we link them to "the finite", or even not at all.
    – exp8j
    Apr 30, 2022 at 7:37
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    You will find all types of answers. Mathematicians have studied infinity the most in recent times. On the opposite extreme of your position is Badiou who says the infinity of set theory is more real than any one thing, as the one is a mistaken concept (or something). Some mathematician I can’t recall has said the discrete and the continuum are two sides of the same coin and neither can be used to explain the other. Other mathematicians use infinity as fundamental to the rest of mathematics (set theory). And a strict finitist might be more in line with you.
    – J Kusin
    Apr 30, 2022 at 13:55
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    In Cohen's words, "The only reality we truly comprehend is that of our own experience. But we have a wonderful ability to extrapolate. The laws of the infinite are extrapolations of our experience with the finite. If there is something infinite, perhaps it is the wonderful intuition we have which allows us to sense what axioms will lead to a consistent and beautiful system such as our contemporary set theory."
    – Ajax
    Apr 30, 2022 at 14:00


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